Dilate (9, 6) using a scale factor of 1/3

Final answer:

Josh has read a total of 45 pages after reading 27 pages in the morning and 18 at night. With 64 pages in the book, he needs to read 19 more pages to finish it.

Explanation:

Josh's book has 64 pages in total. He read 27 pages in the morning and 18 more pages at night. To calculate the number of pages Josh still needs to read to finish the book, we do some quick math:

Therefore, Josh needs to read 19 more pages to finish his book.

Answer:

[tex]a = 2; \ d = 2; \ c=1; \ b=1[/tex]

Step-by-step explanation:

Two functions are inverse where their composition results in a variable only:

[tex]f(g(x))=x[/tex]

So, we have to insert the right numbers in place of letters a, b, c and d, to fulfil this definition. Those value would be: [tex]a = 2; \ d = 2; \ c=1; \ b=1[/tex]

Replacing these values, we have:

[tex]f(x)=x+2[/tex]

[tex]g(x)=1x-2=x-2[/tex]

Applying the composition [tex]f(g(x))[/tex]:

[tex]f(g(x))=\frac{cx-d+a}{b}[/tex]

We observe that with this values, these functions are inverse, because it composition results x.

[tex]f(g(x))=\frac{1x-2+2}{1}=x[/tex]

Therefore, the values are [tex]a = 2; \ d = 2; \ c=1; \ b=1[/tex]

The measure of angle 7 for the given set of parallel lines with given measure of angle 1 as 58 degrees is equal to 122°.

Here line m is parallel to line n and 'q' is the transversal.

In general, when two parallel lines are cut by a transversal, any pair of corresponding exterior angles are congruent.

Angles 1 and 5 are corresponding pair of exterior angles, which are always congruent.

So, the measure of angle 5 is the same as the measure of angle 1, which is 58°.

And measure of angle 5 and angle 7 are linear pair .

This implies,

Measure of ( angle 5  + angle 7 ) = 180°

⇒Measure of angle 7 = 180° - 58°

⇒Measure of angle 7 = 122°

Therefore, the measure of the angle 7 is equal to 122 degrees.

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The above question is incomplete, the complete question is:

The sketch shows two parallel lines cut by a transversal. Angle 1 is 58°. What is the measure of angle 7?

Attached figure.

The three equations that have no solutions are A ,C and F

What is Linear Equation in 1 variable?

The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution

Given data ,

A )

19 + b + 12b – 8 – 5b = 2b – 7 + 3b + 3b – 4

On Simplifying , we get

8b + 11 = 8b - 11

Hence , the option has no solution

B )

4b – 9b – 13 – 6 + 16b = 1 – 8 + 6b + 5b – 12

On Simplifying , we get

11b - 19 = 11b - 19

Adding 19 on both sides , we get

11b = 11b

Divide by 11 on both sides , we get

b = b

Hence , the option has a solution

C )

7 + 7b – 2 – 15b + b = 4b – 5 – 11b + 2 + 10

On Simplifying , we get

- 7b + 5 = - 7b + 7

Hence , the option has no solution

D )

10b + 8b + 9 – 18b + 3 = 5 + 6b – 2b – 12 + 7

On Simplifying , we get

0 + 12 = 4b + 0

4b = 12

Divide by 4 on both sides , we get

b = 3

Hence , the option has a solution

E )

9 – 19b – 9 – 2b + 7b = 4b + 3 + 14 – 4b – 17

On Simplifying , we get

0 - 14b = 0

b = 0

Hence , the option has a solution

F )

8b – 10 + b + 3b + 2 = 7 + 2b + 10b – 18 – 3

On Simplifying , we get

12b - 8 = 12b - 12

Hence , the option has no solution

Therefore , the three equations that have no solutions are A ,C and F

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Answer:

1) Tina interviews the school's soccer team about the exercise habits of  the students at her school. (implying all the students). This means that Tina only goes to the soccer team instead of the whole school to find out the whole school's exercise habit.

2) Alana also counts as representatives, because she did not interview ALL of the teachers, rather just a selected majority (in this case)

5) For Jeremy, he only interviews 5 students from each class rather than all students

Not Representatives: Each person is given a choice of opinion and does not affect other people.

3) Joe talks to fathers of high school students, which could be larger than just 'representatives', and implies a larger group of people, and is not as selective as having representatives

4) Social Media constitutes of a large group of people, generally larger than a school, and if people take time to take the survey, it will generate a larger test-group. Also, everybody answering the survey would take time to think about themselves, and only represent themselves, and not others.

Step-by-step explanation:

hope dis help no cap facts gang gang

Answer:3,888

Step-by-step explanation: hope I helped

A graph that shows a proportional relationship include the following; A. graph A.

In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:

y = kx

Where:

In conclusion, the characteristics for a graph that shows a proportional relationship include the following:

A straight line can be drawn through its points.

The straight line connecting the points passes through the origin.

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Answer with explanation:

⇒The given equation of line in two variable is :

   y = 10 x + 15

If we have to find the solution of the equation of a unique line,as on a line there are infinite number of points lying on it.

So, Line, y=10 x + 15, has infinite number of solution.

Substituting different value of , x we will get different value of y,and by Substituting Different values of y, we will get different values of x.

→→If, x=k, then solution set of line, y=10 x + 15 ,will be,

(x,y)=All the points lying on the line, that is of the form,(k, 10 k +15).

Final answer:

To find the number of girls attending an assembly given a boys-to-girls ratio, divide the total students by the total parts of the ratio and then multiply by the girls' part of the ratio. 300 girls attended the assembly.

Explanation:

Ratios provide us with comparative information. In this case, the ratio of boys to girls is 5 to 6. To find the number of girls, we need to divide the total students by the total parts of the ratio (5 + 6) and then multiply by the girls' part of the ratio:

Calculate total parts of the ratio: 5 (boys) + 6 (girls) = 11.

Divide total students by total parts of the ratio: 550 / 11 = 50.

Multiply by the girls' part of the ratio: 50 (students per part) * 6 (girls) = 300 girls attended the assembly.

Final answer:

To calculate the change in profits over two years with a 5% increase followed by a 3% decrease, the successive percentage change formula was used which resulted in a value 1.85% (approximately).

Explanation:

To solve the question, we need to consider the successive percentage changes in profits over two years. If profits increase by 5% one year and decrease by 3% the following year, we can calculate the overall percentage change using the formula for successive percentage changes.

Let's assume the initial profit is $100. After increasing by 5%, the profit becomes $105. Then, after decreasing by 3%, the profit becomes $105 * (1 - 0.03) = $105 - $3.15 = $101.85. Therefore, over two years, profits are up by 1.85% (approximately).

Answer:

18

Step-by-step explanation:

it is good

The side length of the pyramid's base is approximately 0.7071 inches, and it is an irrational number.

To find the side length of the pyramid's base, we need to use the formula for the volume of a pyramid, which is given by:

[tex]\[ V = \frac{1}{3}Bh \][/tex]

where V is the volume, B is the area of the base, and h is the height of the pyramid.

Given that the volume V  is 0.734 cubic inches and the height h  is 4.41 inches, we can rearrange the formula to solve for the area of the base B :

[tex]\[ B = \frac{3V}{h} \][/tex]

Substituting the given values:

[tex]\[ B = \frac{3 \times 0.734}{4.41} \] \[ B = \frac{2.202}{4.41} \] \[ B \approx 0.5 \text{ square inches} \][/tex]

Now, assuming the base is a square (since we are looking for the side length), the area of the base B  is also equal to the side length squared:

[tex]\[ B = s^2 \][/tex]

where \( s \) is the side length of the base. Therefore:

[tex]\[ s^2 = 0.5 \][/tex]

Taking the square root of both sides:

[tex]\[ s = \sqrt{0.5} \] \[ s \approx 0.7071 \text{ inches} \][/tex]

The side length of the pyramid's base is approximately 0.7071 inches.

To determine if this number is rational or irrational, we consider the definition of rational numbers. A rational number is one that can be expressed as the quotient of two integers. The square root of 0.5 can be rewritten as:

[tex]\[ s = \sqrt{0.5} = \sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} = \frac{1}{\sqrt{2}} \][/tex]

To rationalize the denominator, we multiply the numerator and the denominator by [tex]\( \sqrt{2} \)[/tex]:

[tex]\[ s = \frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2} \][/tex]

Since [tex]\( \sqrt{2} \)[/tex] is an irrational number, the side length s is also irrational because it cannot be expressed as the quotient of two integers.